By James Stewart

This handbook comprises worked-out ideas to each odd-numbered workout in Multivariable Calculus, 8e (Chapters 1-11 of Calculus, 8e).

**Read or Download Student Solutions Manual, Chapters 10-17 for Stewart’s Multivariable Calculus, 8th PDF**

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**Additional resources for Student Solutions Manual, Chapters 10-17 for Stewart’s Multivariable Calculus, 8th**

**Sample text**

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 6 15. = 3 14 34 · = , where = 2 and = 4 − 8 cos 14 1 − 2 cos 3 4 CONIC SECTIONS IN POLAR COORDINATES ¤ ⇒ = 38 . (a) Eccentricity = = 2 (b) Since = 2 1, the conic is a hyperbola. (c) Since “− cos ” appears in the denominator, the directrix is to the left of the focus at the origin.

Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 4 AREAS AND LENGTHS IN POLAR COORDINATES ¤ 25 43. From the ﬁrst graph, we see that the pole is one point of intersection. By zooming in or using the cursor, we ﬁnd the -values of the intersection points to be ≈ 088786 ≈ 089 and − ≈ 225.

10 10 1 2 −10 2 = 5 10 −10 9 cos 5 = 5 · 9 · 2 10 0 10 cos 5 = 18 sin 5 0 = 18 33. The curves intersect when 4 cos = 2 ⇒ cos = 12 ⇒ = ± 3 for − ≤ ≤ . The points of intersection are 2 3 and 2 − 3 . 35. The curves intersect where 2 sin = sin + cos sin = cos ⇒= , 4 ⇒ and also at the origin (at which = 3 4 on the second curve). 34 4 = 0 21 (2 sin )2 + 4 12 (sin + cos )2 34 4 = 0 (1 − cos 2) + 12 4 (1 + sin 2) 4 34 = − 12 sin 2 0 + 12 − 14 cos 2 4 = 12 ( − 1) Copyright 2016 Cengage Learning.